Question

Me piden resolver esta ecuación ∛ (1+√x) + ∛ (1-√x) = ∛5

Answer 1

Solución:

∛(1 + √x) + ∛(1 - √x) = ∛5
(∛(1 + √x) + ∛(1 - √x))³ = (∛5)³

Utilizar:  (a + b)³ = a³ + b³ + 3ab(a + b)

(∛(1 + √x))³ + (∛(1 - √x))³ + 3∛(1 + √x)∛(1 - √x)(∛(1 + √x) + ∛(1 - √x)) = 5
1 + √x + 1 - √x + 3∛((1 + √x)(1 - √x))(∛5) = 5 
2 + 3∛(1² - √x²)(∛5) = 5
3∛((1 - x)(5)) = 5 - 2
3∛(5(1 - x)) = 3
∛(5(1 - x)) = 3 / 3
∛(5(1 - x)) = 1
(∛(5(1 - x)))³ = 1³
5(1 - x) = 1
5 - 5x = 1
5 - 1 = 5x
4 = 5x
4 / 5 = x

x = 4 / 5